Quasioptimality of maximum-volume cross interpolation of tensors
Quasioptimality of maximum-volume cross interpolation of tensors
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DOI：
10.1016/j.laa.2014.06.006
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发表时间：
2013-05
影响因子：
1.1
通讯作者：
D. Savostyanov
中科院分区：
文献类型：
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作者：
D. Savostyanov
我们考虑一个交叉插值的张量列车格式的高维数组。我们证明，最大体积的选择的插值集提供了准最优的插值精度，不同的最佳可能的精度的因素，不随尺寸呈指数增长。对于嵌套插值集，我们证明了插值性质，并提出了贪婪交叉插值算法。我们证明了理论结果，并测量所提出的算法的速度和精度与数值实验。
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension. For nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms. We justify the theoretical results and measure speed and accuracy of the proposed algorithm with numerical experiments.